Hi @vickie1320, unfortunately, Trismus or jaw muscle spasms that are so strong the mouth can’t be opened, can be a common side effect from head/neck cancer with treatments with radiation.
I’m so sorry your husband is having to deal with this along with everything else he’s been going through with his cancer. If he’s doing the suggested exercises this should help to keep his muscles flexible. But it’s important to continue with these even if he’s not having symptoms.

Has he talked with his doctor about this? I think you mentioned in another post that there is a dentist associated with the cancer clinic? That doctor would be a good source to consult with as they would be familiar with the condition and may have some good suggestions for your husband.
Consulting with an oral surgeon or a speech pathologist could be other valuable source for helping to get the mouth functioning properly again.

@hrhwilliam has experience with throat cancer, radiation and reconstructive jaw surgery. He shared his story with us in this discussion. If you haven’t already, I think this would be a helpful conversation to follow. The link is posted below.

~Radiation side effects with H&N cancer. When will they ever end?
https://connect.mayoclinic.org/discussion/radiation-side-effects-when-will-they-ever-end/
I found a couple of comprehensive websites for you about developing Trismus following radiation treatment. You already mentioned that your husband is doing some of these exercises but hopefully there are a few new things for you to try.
https://headandneck.org/trismus/
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https://www.mskcc.org/cancer-care/patient-education/trismus
Has your husband tried some warm compresses, such as warm washcloths or wrapped hot water bottle…not a heating pad?